The 34-year-old Dunne made his debut against Greece in 2000 and won 80 caps, scoring eight goals.
"Retiring from international football has been an extremely difficult decision for me to make," Dunne told the promoted west London club's official website.
"I have represented Ireland since I was 15 years of age, and have thoroughly enjoyed all the highs and lows that have come with playing for my country."
Ireland are now coached by Martin O'Neill, Dunne's former manager at Aston Villa, while the QPR defender also played with current assistant coach Roy Keane who was national team captain.
"Richard has been a remarkable player for both club and country," O'Neill said. "He has consistently given 100 percent every time he has been called on by his country."
(Reporting by Tom Hayward; Editing by Ken Ferris)
